When a black hole is perturbed, it rings out in gravitational waves. Measuring these gravitational waves is akin to taking the black hole’s fingerprint: the complex frequency spectrum of the ringing waves depends uniquely on the underlying spacetime structure of the black hole. Because different gravitational theories predict different spacetime structures, these spectral fingerprints can reveal the identity of the theory governing our universe. The LIGO detectors are now observing these ringing waves and placing the first constraints on black hole spacetimes. In this talk, we’ll survey the rapidly evolving state of the art in analyses of such ringing signals, highlight the strongest constraints achieved so far, and explore the many theoretical challenges and ongoing debates driving the field.